On the probability of generating a monolithic group
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A group L is primitive monolithic if L has a unique minimal normal subgroup, N , and trivial Frattini subgroup. By PL,N(k) we denote the conditional probability that k randomly chosen elements of L generate L , given that they project onto generators for L/N. In this article we show that PL,N(k) is controlled by PY,S(2), where N≅Sr and Y is a 2-generated almost simple group with socle S that is contained in the normalizer in L of the first direct factor of N . Information aboutPL,N(k) for L primitive monolithic yields various types of information about the generation of arbitrary finite and profinite groups.
Detomi , E , Lucchini , A & Roney-Dougal , C M 2014 , ' On the probability of generating a monolithic group ' Journal of Algebra , vol 407 , pp. 413-433 . DOI: 10.1016/j.jalgebra.2014.03.010
Journal of Algebra
Copyright 2014, the authors. This is an open access article under the CC-BY license. http://creativecommons.org/licenses/by/3.0/
This research was supported through EPSRC grant EP/I03582X/1. The APC was paid through RCUK open access block grant funds.
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